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Physical Review A

Gain without population inversion in a yoked superfluorescence scheme

Luqi Yuan, Anatoly A. Svidzinsky

Published Mar 29, 2012• 11 citations
Publisher

Abstract

We consider a medium composed of three-level (cascade scheme) atoms prepared with coherence between the upper and the ground states (a yoked superfluorescence system). We obtain an analytical solution for propagation of seed pulses which are resonant with the upper and lower transitions for arbitrary level populations and pulse shapes. We find that if the initial coherence is large enough and the intermediate level is populated the system can have gain without population inversion. Coherence can also yield gain suppression in the inverted medium. We obtain conditions for the gain in terms of level populations and coherence.

DOI
10.1103/physreva.85.033836

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We consider a medium composed of three-level (cascade scheme) atoms prepared with coherence between the upper and the ground states (a yoked superfluorescence system). We obtain an analytical solution for propagation of seed pulses which are resonant with the upper and lower transitions for arbitrary level populations and pulse shapes. We find that if the initial coherence is large enough and the intermediate level is populated the system can have gain without population inversion. Coherence can also yield gain suppression in the inverted medium. We obtain conditions for the gain in terms of level populations and coherence.
A superfluorescence effect in a V-type medium with initial Raman inversion, driven by a strong coherent field on one of the transitions, is studied analytically and numerically. It is shown that the collective spontaneous emission evolves in the presence of a minor population of an upper state of a superfluorescent transition. In the limit of the Rabi frequency of a driving field large compared to that of a superfluorescent pulse, the system of two equations for the fields and density-matrix equations for three states of the medium is reduced to Maxwell-Bloch equations for an effective two-level system. The shape of a superfluorescent pulse is perfectly described in terms of a slowly varying envelope function (which is a solution of the Maxwell-Bloch equations), filled with fast oscillations associated with Rabi floppings on the driving transition. In the average, i.e., after integrating over a period of Rabi oscillations, the upper superfluorescent state is populated less than other states, such that the phenomenon may be called ``superfluorescence without inversion'' by analogy with lasing without inversion.
We study the propagation of a bichromatic field in three-level and four-level media. In the case of a three-level medium, we consider the \ensuremath{\Lambda} configuration and demonstrate that if the upper level is not empty there is a critical value for the low-frequency coherence such that below this threshold and for intense fields, coherent bleaching occurs. This implies a sharp reduction of the field absorption and the fluorescence emission whereas above this threshold a parametric instability takes place. It corresponds to an amplification of the field that does not need a population inversion between the optical transitions. Finally we prove that the field alone cannot create a low-frequency coherence exceeding this threshold. Therefore we analyze the double-\ensuremath{\Lambda} configuration involving a four-level medium in which the upper and lower pairs of atomic levels have a low-frequency separation while optical transitions take place between the two pairs of states. An intense bichromatic field that is resonant with one upper state and the lower levels and a weak bichromatic field resonant with the other upper state and the same two lower states are sent into the medium. We analyze the limit in which the low-frequency coherence created between the lower pair of states has a relaxation time which is large. Then there will be population trapping in the lower states leading to coherent bleaching if there is no inversion between the upper levels but there will be amplification if there is inversion between the upper levels. In this way amplification at the optical transitions without population inversion between these states is realized.
We analyze the temporal development of a seed signal propagating in an ensemble of three-level atoms initially pumped by a two- photon excitation pulse. In an incoherently prepared system, the medium acts as a two-level system. Such a system is scale- invariant and therefore its dynamics are uniquely determined by the value of (alpha) L. On the other hand, a coherently prepared system is not scale invariant, leading to more complicated dynamics. We show that at low optical gain the amplification is reduced when the pumping is coherent. We further show that at high inversion there is an exponential increase in the radiation emitted from the lower transition in an initially prepared coherent system.
Numerical simulations of an extended sample of three-level atoms with slow dipole dephasing exhibit a superfluorescent pulse shortly after incoherent pumping begins. The operator Maxwell-Bloch equations are simulated by classical Langevin equations. The counterpropagating fields are solved for in the (one-dimensional) limit of the Fresnel number near unity, with open-end boundary conditions. An initial, ``quiet'' buildup of the inversion is followed by superfluorescence. Oscillation of the populations, coherences, and fields is observed. The superfluorescence delay time is compared with analytical predictions made in the linear regime. A transition to amplified spontaneous emission is found as the pump rate is decreased.
We obtain the gain of the probe field at multiple frequencies in a closed three-level V-type system using a frequency-modulated pump field. There is no associated population inversion among the atomic states of the probe transition. We describe both the steady-state and transient dynamics of this system. Under suitable conditions, the system exhibits a large gain simultaneously at a series of frequencies far removed from resonance. Moreover, the system can be tailored to exhibit multiple frequency regimes where the probe experiences anomalous dispersion accompanied by negligible gain or absorption over a large bandwidth, a desirable feature for obtaining superluminal propagation of pulses with negligible distortion.
An analysis is made of the conditions for the generation of superfluorescence pulses in an inverted medium of electron—hole pairs in a semiconductor. It is shown that strong optical amplification in laser semiconductor amplifiers characterised by α L ≫ 1 (α is the small-signal gain and L is the amplifier length) leads to suppression of phase relaxation of the medium during the initial stages of evolution of superfluorescence and to formation of a macroscopic dipole from electron—hole pairs. Cooperative emission of radiation in this system results in generation of a powerful ultrashort pulse of the optical gain, which interacts coherently with the semiconductor medium. It is shown that coherent pulsations of the optical field, observed earlier by the author in Q -switched semiconductor lasers, are the result of superfluorescence and of the coherent interaction between the optical field and the medium.